54 pages, Latex, 2 figures, v2: Anzatz for momentum in proof of Gubser-Mitra conjecture corrected; factor of 2 in symplectic form corrected; several typos in formulas corrected; v3: revised argument concerning horizon gauge condition on p. 10; typos corrected and several minor changes; reference added; v4: formula (86) for \E corrected, footnote added
We establish a new criterion for the dynamical stability of black holes in $D \geq 4$ spacetime dimensions in general relativity with respect to axisymmetric perturbations: Dynamical stability is equivalent to the positivity of the canonical energy, $\E$, on a subspace, $\mathcal T$, of linearized solutions that have vanishing linearized ADM mass, momentum, and angular momentum at infinity and satisfy certain gauge conditions at the horizon. This is shown by proving that---apart from pure gauge perturbations and perturbations towards other stationary black holes---$\E$ is nondegenerate on $\mathcal T$ and that, for axisymmetric perturbations, $\E$ has positive flux properties at both infinity and the horizon. We further show that $\E$ is related to the second order variations of mass, angular momentum, and horizon area by $\E = δ^2 M - \sum_A Ω_A δ^2 J_A - \fracκ{8π} δ^2 A$, thereby establishing a close connection between dynamical stability and thermodynamic stability. Thermodynamic instability of a family of black holes need not imply dynamical instability because the perturbations towards other members of the family will not, in general, have vanishing linearized ADM mass and/or angular momentum. However, we prove that for any black brane corresponding to a thermodynamically unstable black hole, sufficiently long wavelength perturbations can be found with $\E < 0$ and vanishing linearized ADM quantities. Thus, all black branes corresponding to thermodynmically unstable black holes are dynamically unstable, as conjectured by Gubser and Mitra. We also prove that positivity of $\E$ on $\mathcal T$ is equivalent to the satisfaction of a "local Penrose inequality," thus showing that satisfaction of this local Penrose inequality is necessary and sufficient for dynamical stability.
The Penrose process of an extremal braneworld black hole is studied. We analyze the Penrose process by two massive spinning particles collide near the horizon. By calculating the maximum energy extraction efficiency of this process, it turns out that the maximal efficiency increases as the tilde charge parameter $d$ of the braneworld blackhole decreases. Interestingly, for the negative value of $d$, the efficiency can be even larger than the Kerr case.
The universal thermodynamic relations between corrections to entropy and extremality for various black holes solutions have been studied. In this regard, we hereby consider a number of different black brane solutions in different structures for perturbative corrections to general relativity. These are, namely, black brane solution in Rastall AdS massive gravity, Einstein-Yang-Mills AdS black brane solution in massive gravity and general anisotropic black brane in Horava-Lifshitz gravity. We calculate both the entropy and extremality bound by introducing a small constant correction to the actio…
In this paper, we study the acoustic black hole emerged from the nonextremal black D3-brane, based on the holographic approaches in constructing the acoustic black hole in asymptotically Anti de-Sitter spacetime (AAdS) and the effective hydrodynamic description of the nonextremal black D3-brane. We show that the holographic dual description of the acoustic black hole appeared on the timelike cutoff surface in the nonextremal black D3-brane also exist. The duality includes the dynamical connection between the acoustic black hole and the bulk gravity, a universal equation relating the Hawking-li…
We perturbatively construct asymptotically $\mathbb{R}^{1,3}\times\mathbb{T}^2$ black branes with multiple inhomogeneous directions and show that some of them are thermodynamically preferred over uniform branes in both the microcanonical and canonical ensembles. This demonstrates that, unlike five-dimensional black strings, the instability of some unstable black branes has a plausible endpoint that does not require a violation of cosmic censorship.
Following a recent approach, complete and analytic solutions (brane and bulk) of regular black holes are shown in a brane context. The metrics are regular both on the four-dimensional brane and in the five-dimensional bulk. Like many brane world scenarios, the bulk spacetime is asymptotically anti-de Sitter. On the other hand, a de Sitter core on the brane avoids the singularity inside the event horizon, providing then well-known regular black holes on the brane. From the bulk perspective, the regular black holes are five-dimensional objects, with the event horizon extending to the extra dimen…
It is shown that, in contrast to the case of extreme 4d dilatonic black holes, 4d neutral dilatonic black holes with horizon singularities can not be interpreted as nonsingular nondilatonic black p-branes in (4+p) dimensions, regardless of the number of extra dimensions p. That is, extra dimensions do not remove naked singularities of 4d neutral dilatonic black holes.
Black p-brane Thermodynamics without Constructing Solutions
Center for Joint Quantum Studies, Department of Physics, School of Science, Tianjin University（天津大学理学院物理系联合量子研究中心）；The International Joint Institute of Tianjin University, Fuzhou, Tianjin University（天津大学福州国际联合学院）
我们探讨了在黑洞块中定位膜的可能性。我们明确地研究了BHTZ和Schwarzschild-anti de Sitter（AdS）黑洞的情况。我们的结果是，在这些情况下，膜不能仅仅由膜张力支撑，必须在膜上引入其他形式的物质。我们发现类完美流体的解决方案，遵守特殊的状态方程。对于BHTZ体几何的情况下，状态方程采取的正是一个'' Chaubergin气体''的形式，这是相关的膜上下文。在Schwarzschild-AdS的情况下，我们找到了新的状态方程，当膜位于视界附近时，这些状态方程简化为Chaubergin形式。
