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We study the P – V criticality and phase transition in the extended phase space of anti-de Sitter (AdS) black holes in higher-dimensional de Rham, Gabadadze and Tolley (dRGT) massive gravity, treating the cosmological constant as pressure and the corresponding conjugate quantity is interpreted as thermodynamic volume. Besides the usual small/large black hole phase transitions, the interesting thermodynamic phenomena of reentrant phase transitions (RPTs) are observed for black holes in all d ≥ 6 -dimensional spacetime when the coupling coefficients c i m 2 of massive potential satisfy some certain conditions.

In General Relativity, addressing coupling to a non-linear electromagnetic field, together with a negative cosmological constant, we obtain the general static spherical symmetric black hole solution with magnetic charges, which is asymptotic to anti-de Sitter (AdS) space-times. In particular, for a degenerate case the solution becomes a Hayward–AdS black hole, which is regular everywhere in the full space-time. The existence of such a regular black hole solution preserves the weak energy condition, while the strong energy condition is violated. We then derive the first law and the Smarr formula of the black hole solution. We further discuss its thermodynamic properties and study the critical phenomena in the extended phase space where the cosmological constant is treated as a thermodynamic variable as well as the parameter associated with the non-linear electrodynamics. We obtain many interesting results such as: the Maxwell equal area law in the P - V (or S - T ) diagram is violated and consequently the critical point ( T ∗ , P ∗ ) of the first order small–large black hole transition does not coincide with the inflection point ( T c , P c ) of the isotherms; the Clapeyron equation describing the coexistence curve of the Van der Waals (vdW) fluid is no longer valid; the heat capacity at constant pressure is finite at the critical point; the various exponents near the critical point are also different from those of the vdW fluid.

The aim of this paper is to study the quantum tunneling process for charged vector particles through the horizons of more generalized black holes by using the Proca equation. For this purpose, we consider a pair of charged accelerating and rotating black holes with Newman–Unti–Tamburino parameter and a black hole in 5D gauged super-gravity theory, respectively. Further, we study the tunneling probability and corresponding Hawking temperature for both black holes by using the WKB approximation. We find that our analysis is independent of the particles species whether or not the background black hole geometries are more generalized.

We explore the quadratic form of the f(R)=R+bR2 gravitational theory to derive rotating N-dimensions black hole solutions with ai,i≥1 rotation parameters. Here, R is the Ricci scalar and b is the dimensional parameter. We assumed that the N-dimensional spacetime is static and it has flat horizons with a zero curvature boundary. We investigated the physics of black holes by calculating the relations of physical quantities such as the horizon radius and mass. We also demonstrate that, in the four-dimensional case, the higher-order curvature does not contribute to the black hole, i.e., black hole does not depend on the dimensional parameter b, whereas, in the case of N>4, it depends on parameter b, owing to the contribution of the correction R2 term. We analyze the conserved quantities, energy, and angular-momentum, of black hole solutions by applying the relocalization method. Additionally, we calculate the thermodynamic quantities, such as temperature and entropy, and examine the stability of black hole solutions locally and show that they have thermodynamic stability. Moreover, the calculations of entropy put a constraint on the parameter b to be b<116Λ to obtain a positive entropy.

We review a special class of N=2 supergravity model that interpolates all the single-dilaton truncations of the maximal SO(8) gauged supergravity. We also provide explicit non-extremal, charged black hole solutions and their supersymmetric limits, asymptotic charges, thermodynamics and boundary conditions. We also discuss a suitable Hamilton–Jacobi formulation and related BPS flow equations for the supersymmetric configurations, with an explicit form for the superpotential function. Finally, we briefly analyze certain models within the class under consideration as consistent truncations of the maximal, N=8 gauged supergravity in four dimensions.

We review a special class of N =2 supergravity model that interpolates all the single-dilaton truncations of the maximal SO(8) gauged supergravity. We also provide explicit non-extremal, charged black hole solutions and their supersymmetric limits, asymptotic charges, thermodynamics and boundary conditions. We also discuss a suitable Hamilton–Jacobi formulation and related BPS flow equations for the supersymmetric configurations, with an explicit form for the superpotential function. Finally, we briefly analyze certain models within the class under consideration as consistent truncations of the maximal, N =8 gauged supergravity in four dimensions.

In this thesis, we describe numerical spherical collapse solutions to a \"modified gravity'' theory, Einstein dilaton Gauss-Bonnet (EdGB) gravity. Of the class of all known modified gravity theories, EdGB gravity has attracted recent attention due to speculations that the theory may have a classically well-posed initial value formulation and yet also exhibit stable scalarized black hole solutions (what makes this surprising is the plethora of black hole \"no hair theorems'', the assumptions behind which EdGB gravity manages to avoid). If EdGB gravity indeed possess these properties, it would be an ideal theory to perform model-selection tests against general relativity (GR) in binary black hole merger using gravitational waves. Furthermore, the theory is an important member of the so-called ``Horndeski theories'', which have been invoked to construct, e.g. nonsingular black hole and cosmological solutions, and to address the classical flatness and horizon problems of the early universe.In constructing numerical solutions to EdGB gravity (without any approximations beyond the restriction to spherically symmetric configurations), we are able to carefully examine various claims made in the literature about EdGB gravity, perhaps most importantly whether or not the theory admits a classically well-posed initial value problem. One conclusion of these studies has been, at least in spherical collapse, EdGB gravity can dynamically lose hyperbolicity, which shows EDGB gravity is fundamentally of \"mixed type\". Mixed type problems appear in earlier problems in mathematical physics, perhaps most notably in the problem of steady state, inviscid, compressible fluid flow. The loss of hyperbolicity and subsequent formation of \"elliptic regions'' outside of any sort of horizon implies that the theory violates cosmic censorship, broadly defined. Arguably it is clear that this result is gauge invariant, although we do not formulate a rigorous proof that this is so. In addition to discussing the hyperbolicity of EdGB gravity, we discuss several other interesting features to the numerical solutions, including the formation of scalarized black hole solutions in the theory, at least for certain parameter ranges for the theory and certain open sets of initial data.

We review the status of the integrability and solvability of the geodesics equations of motion on symmetric coset spaces that appear as sigma models of supergravity theories when reduced over respectively the timelike and spacelike direction. Such geodesic curves describe respectively timelike and spacelike brane solutions. We emphasize the applications to black holes.

A bstract We exploit the recently proposed correspondence between gravitational perturbations and quantum Seiberg-Witten curves to compute the spectrum of quasi-normal modes of asymptotically flat Kerr Newman black holes and establish detailed gauge/gravity dictionaries for a large class of black holes, D-branes and fuzzballs in diverse dimensions. QNM frequencies obtained from the quantum periods of SU(2) N = 2 SYM with N f = 3 flavours are compared against numerical results, WKB (eikonal) approximation and geodetic motion showing remarkable agreement. Starting from the master example relating quasi-normal modes of Kerr-Newman black holes in AdS 4 to SU(2) gauge theory with N f = 4, we illustrate the procedure for some simple toy-models that allow analytic solutions. We also argue that the AGT version of the gauge/gravity correspondence may give precious hints as to the physical/geometric origin of the quasi-normal modes/Seiberg-Witten connection and further elucidate interesting properties (such as tidal Love numbers and grey-body factors) that can help discriminating black holes from fuzzballs.

A bstract We study classical closed bosonic strings probing the near-horizon region of a non-extremal black hole and show that this corresponds to understanding string theory in the Carroll regime. This is done by first performing a Carroll expansion and then a near-horizon expansion of a closed relativistic string, subsequently showing that they agree. Concretely, we expand the phase space action in powers of c 2 , where c is the speed of light, assuming that the target space admits a string Carroll expansion (where two directions are singled out) and show that there exist two different Carroll strings: a magnetic and an electric string. The magnetic string has a Lorentzian worldsheet, whereas the worldsheet of the electric string is Carrollian. The geometry near the horizon of a four-dimensional (4D) Schwarzschild black hole takes the form of a string Carroll expansion (a 2D Rindler space fibred over a 2-sphere). We show that the solution space of relativistic strings near the horizon bifurcates and the two sectors precisely match with the magnetic/electric Carroll strings with an appropriate target space. Magnetic Carroll strings near a black hole shrink to a point on the two-sphere and either follow null geodesics or turn into folded strings on the 2D Rindler spacetime. Electric Carroll strings wrap the two-sphere and follow a massive geodesic in the Rindler space. Finally, we show that 4D non-extremal Kerr and Reissner-Nordström black holes also admit string Carroll expansions near their outer horizons, indicating that our formulation extends to generic non-extremal black holes.