Motivated by recent studies of long-range forces between identical black holes, we extend these c... more Motivated by recent studies of long-range forces between identical black holes, we extend these considerations by investigating the forces between two nonidentical black holes. We focus on classes of theories where charged black holes can have extremal limits that are not BPS. These theories, which live in arbitrary spacetime dimension, comprise gravity coupled to N 2-form field strengths and (N -1) scalar fields. In the solutions we consider, each field strength carries an electric charge. The black hole solutions are governed by the SLðN þ 1; RÞ Toda equations. In four dimensions, the black hole solutions in the SLð3; RÞ example are equivalent to the "Kaluza-Klein dyons." We find that any pair of such extremal black holes that are not identical (up to overall scaling) will repel one another. We also show that there can exist pairs of non-extremal, nonidentical black holes which obey a zero-force condition. Finally, we find indications of similar results in the higher examples, such as SLð4; RÞ.
A 12-year-old pre-menarchal girl presented to our emergency department with acute urinary retenti... more A 12-year-old pre-menarchal girl presented to our emergency department with acute urinary retention for last eight hours. She admitted having difficulty in micturition for last one month. She denied any other significant past medical or surgical history. During per urethral catheterization a non-tender lump which used to increase on Valsalva manoeuvre was noted in the perineum. Abdominal ultrasonography and magnetic resonance imaging (MRI) showed a large haematocolpos compressing the urethra. She underwent hymenotomy with evacuation of collected menstrual blood. Post procedure recovery was uneventful and she was able to pass urine with normal stream subsequently.
The extremal Reissner-Nordström black hole admits a conformal inversion symmetry, in which the me... more The extremal Reissner-Nordström black hole admits a conformal inversion symmetry, in which the metric is mapped into itself under an inversion of the radial coordinate combined with a conformal rescaling. In the rotating generalisation, Couch and Torrence showed that the Kerr-Newman metric no longer exhibits a conformal inversion symmetry, but the radial equation arising in the separation of the massless Klein-Gordon equation admits a mode-dependent inversion symmetry, where the radius of inversion depends upon the energy and azimuthal angular momentum of the mode. It was more recently shown that the static 4-charge extremal black holes of STU supergravity admit a generalisation of the conformal inversion symmetry, in which the conformally-inverted metric is a member of the same 4-charge black hole family but with transformed charges. In this paper we study further generalisations of these inversion symmetries, within the general class of extremal STU supergravity black holes. For the rotating black holes, where again the massless Klein-Gordon equation is separable, we show that examples with four electric charges exhibit a generalisation of the Couch-Torrence symmetry of the radial equation. Now, as in the conformal inversion of the static specialisations, the inversion of the radial equation maps it to the radial equation for a rotating black hole with transformed electric charges. We also study the inversion transformations for the general case of extremal BPS STU black holes carrying eight charges (4 electric plus 4 magnetic), and argue that analogous generalisations of the inversion symmetries exist both for the static and the rotating cases.
We present a construction of the most general BPS black holes of STU supergravity (N = 2 supersym... more We present a construction of the most general BPS black holes of STU supergravity (N = 2 supersymmetric D = 4 supergravity coupled to three vector supermultiplets) with arbitrary asymptotic values of the scalar fields. These solutions are obtained by acting with a subset of the global symmetry generators on STU BPS black holes with zero values of the asymptotic scalars, both in the U-duality and the heterotic frame. The solutions are parameterized by fourteen parameters: four electric and four magnetic charges, and the asymptotic values of the six scalar fields. We also present BPS black hole solutions of a consistently truncated STU supergravity, which are parameterized by two electric and two magnetic charges and two scalar fields. These latter solutions are significantly simplified, and are very suitable for further explicit studies. We also explore a conformal inversion symmetry of the Couch-Torrence type, which maps any member of the fourteen-parameter family of BPS black holes to another member of the family. Furthermore, these solutions are expected to be valuable in the studies of various swampland conjectures in the moduli space of string compactifications.
CERN Document Server (European Organization for Nuclear Research), Jul 1, 2022
Motivated by recent studies of long-range forces beween identical black holes, we extend these co... more Motivated by recent studies of long-range forces beween identical black holes, we extend these considerations by investigating the forces between two non-identical black holes. We focus on classes of theories where charged black holes can have extremal limits that are not BPS. These theories, which live in arbitrary spacetime dimension, comprise gravity coupled to N 2-form field strengths and (N -1) scalar fields. In the solutions we consider, each field strength carries an electric charge. The black hole solutions are governed by the SL(N + 1, R) Toda equations. In four dimensions the black-hole solutions in the SL(3, R) example are equivalent to the "Kaluza-Klein dyons." We find that any pair of such extremal black holes that are not identical (up to overall scaling) repel one another. We also show that there can exist pairs of non-extremal, non-identical black holes which obey a zero-force condition. Finally, we find indications of similar results in the higher examples, such as SL(4, R).
We find the equations of motion of membranes dual to the black holes in Einstein-Gauss-Bonnet (EG... more We find the equations of motion of membranes dual to the black holes in Einstein-Gauss-Bonnet (EGB) gravity to leading order in 1/D in the large D regime. We also find the metric solutions to the EGB equations to first subleading order in 1/D in terms of membrane variables. We propose a world volume stress tensor for the membrane whose conservation equations are equivalent to the leading order membrane equations. We work out the light quasi-normal mode spectrum of static black holes in EGB gravity from the linearised fluctuations of static, round membranes. Also, the effective equations for stationary black holes and the spectrum of linearised spectrum about black string configurations has been obtained using the membrane equation for EGB gravity. All our results are worked out to linear order in the Gauss-Bonnet parameter.
We revisit the study of the phase structure of higher spin black holes carried out in arXiv: 1210... more We revisit the study of the phase structure of higher spin black holes carried out in arXiv: 1210.0284 using the "canonical formalism". In particular we study the low as well as the high temperature regimes. We show that the Hawking-Page transition takes place in the low temperature regime. The thermodynamically favoured phase changes from conical surplus to black holes and then again to conical surplus as we increase temperature. We then show that in the high temperature regime the diagonal embedding gives the appropriate description. We also give a map between the parameters of the theory near the IR and UV fixed points with the effect that the "good" solutions near IR fixed point map to the "bad" solutions near the UV fixed point and vice versa.
We revisit the study of the phase structure of higher spin black holes carried out in arXiv: 1210... more We revisit the study of the phase structure of higher spin black holes carried out in arXiv: 1210.0284 using the “canonical formalism”. In particular we study the low as well as the high temperature regimes. We show that the Hawking-Page transition takes place in the low temperature regime. The thermodynamically favoured phase changes from conical surplus to black holes and then again to conical surplus as we increase temperature. We then show that in the high temperature regime the diagonal embedding gives the appropriate description. We also give a map between the parameters of the theory near the IR and UV fixed points with the effect that the “good” solutions near IR fixed point map to the “bad” solutions near the UV fixed point and vice versa. E-mail: [email protected] E-mail: [email protected]
It has recently been demonstrated that black hole dynamics at large D is dual to the motion of a ... more It has recently been demonstrated that black hole dynamics at large D is dual to the motion of a probe membrane propagating in the background of a spacetime that solves Einstein’s equations. The equation of motion of this membrane is determined by the membrane stress tensor. In this paper we ‘improve’ the membrane stress tensor derived in earlier work to ensure that it defines consistent probe membrane dynamics even at finite D while reducing to previous results at large D. Our improved stress tensor is the sum of a Brown York term and a fluid energy momentum tensor. The fluid has an unusual equation of state; its pressure is nontrivial but its energy density vanishes. We demonstrate that all stationary solutions of our membrane equations are produced by the extremization of an action functional of the membrane shape. Our action is an offshell generalization of the membrane’s thermodynamical partition function. We demonstrate that the thermodynamics of static spherical membranes in ...
It has recently been demonstrated that the dynamics of black holes at large D can be recast as a ... more It has recently been demonstrated that the dynamics of black holes at large D can be recast as a set of non gravitational membrane equations. These membrane equations admit a simple static solution with shape S D-p-2 ×R p,1 . In this note we study the equations for small fluctuations about this solution in a limit in which amplitude and length scale of the fluctuations are simultaneously scaled to zero as D is taken to infinity. We demonstrate that the resultant nonlinear equations, which capture the Gregory-Laflamme instability and its end point, exactly agree with the effective dynamical 'black brane' equations of Emparan Suzuki and Tanabe. Our results thus identify the 'black brane' equations as a special limit of the membrane equations and so unify these approaches to large D black hole dynamics.
We report on the results of the E06-014 experiment performed at Jefferson Lab in Hall A, where a ... more We report on the results of the E06-014 experiment performed at Jefferson Lab in Hall A, where a precision measurement of the twist-3 matrix element d2 of the neutron (d n 2 ) was conducted. The quantity d n 2 represents the average color Lorentz force a struck quark experiences in a deep inelastic electron scattering event off a neutron due to its interaction with the hadronizing remnants. This color force was determined from a linear combination of the third moments of the 3 He spin structure functions, g1 and g2, after nuclear corrections had been applied to these moments. The structure functions were obtained from a measurement of the unpolarized cross section and of double-spin asymmetries in the scattering of a longitudinally polarized electron beam from a transversely and a longitudinally polarized 3 He target. The measurement kinematics included two average Q 2 bins of 3.2 GeV 2 and 4.3 GeV 2 , and Bjorken-x 0.25 ≤ x ≤ 0.90 covering the deep inelastic and resonance regions. We have found that d n 2 is small and negative for Q 2 = 3.2 GeV 2 , and even smaller for Q 2 = 4.3 GeV 2 , consistent with the results of a lattice QCD calculation. The twist-4 matrix element f n 2 was extracted by combining our measured d n 2 with the world data on the first moment in x of g n 1 , Γ n 1 . We found f n 2 to be roughly an order of magnitude larger than d n 2 . Utilizing the extracted d n 2 and f n 2 data, we separated the Lorentz color force into its electric and magnetic components, F y,n E and F y,n B , and found them to be equal and opposite in magnitude, in agreement with the predictions from an instanton model but not with those from QCD sum rules. Furthermore, using the measured double-spin asymmetries, we have extracted the virtual photon-nucleon asymmetry on the neutron A n 1 , the structure function ratio g n 1 /F n 1 , and the quark ratios (∆u+∆ū)/(u+ū) and (∆d+∆ d)/(d+ d). These results were found to be consistent with DIS world data and with the prediction of the constituent quark model but at odds with the perturbative quantum chromodynamics predictions at large x.
We study SO(d + 1) invariant solutions of the classical vacuum Einstein equations in p + d + 3 di... more We study SO(d + 1) invariant solutions of the classical vacuum Einstein equations in p + d + 3 dimensions. In the limit d → ∞ with p held fixed we construct a class of solutions labelled by the shape of a membrane (the event horizon), together with a 'velocity' field that lives on this membrane. We demonstrate that our metrics can be corrected to nonsingular solutions at first sub-leading order in 1 d if and only if the membrane shape and 'velocity' field obey equations of motion which we determine. These equations define a well posed initial value problem for the membrane shape and this 'velocity' and so completely determine the dynamics of the black hole. They may be viewed as governing the non-linear dynamics of the light quasi normal modes of Emparan, Suzuki and Tanabe.
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Papers by Arunabha Saha