A note on the circle actions on Einstein manifolds

2001 ◽  
Vol 63 (1) ◽  
pp. 83-91
Author(s):  
Seungsu Hwang
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Scalar Curvature ◽  
Einstein Manifold ◽  
Orbit Space ◽  
Circle Action ◽  
Fundamental Result ◽  
Einstein Manifolds ◽  
Circle Actions ◽  
Zero Scalar Curvature

A fundamental result in the theory of black holes due to Hawking asserts that the event horizon of a black hole in the stationary space-time is a 2-sphere topologically. In this article we prove the Riemannian analogue of Hawking's result. In other words, we prove that each bolt of a 4-dimensional complete noncompact Einstein manifold of zero scalar curvature admitting a semifree isometric circle action is a 2-sphere topologically. We also study the structure of the orbit space of an Einstein manifold admitting a free isometric circle action.

scholarly journals A note on the volume of ∇-Einstein manifolds with skew-torsion

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ioannis Chrysikos
Keyword(s):  
Scalar Curvature ◽  
Riemannian Manifolds ◽  
Einstein Manifold ◽  
Einstein Manifolds ◽  
First Variation ◽  
Metric Connection ◽  
The First Variation

AbstractWe study the volume of compact Riemannian manifolds which are Einstein with respect to a metric connection with (parallel) skew-torsion. We provide a result for the sign of the first variation of the volume in terms of the corresponding scalar curvature. This generalizes a result of M. Ville [15] related with the first variation of the volume on a compact Einstein manifold.

scholarly journals SEIBERG–WITTEN INVARIANTS OF 4-MANIFOLDS WITH FREE CIRCLE ACTIONS

2001 ◽  
Vol 03 (03) ◽  
pp. 341-353 ◽  
Author(s):  
SCOTT BALDRIDGE
Keyword(s):  
Orbit Space ◽  
Total Space ◽  
Circle Action ◽  
Witten Invariant ◽  
Circle Bundle ◽  
Circle Actions ◽  
3 Dimensional

The main results of this paper describes a formula for the Seiberg–Witten invariant of a 4-manifold which admits a nontrivial free circle action. We use this theorem to produce a nonsymplectic 4-manifold with a free circle action whose orbit space fibers over circle. We also describe a nontrivial 3-manifold which is not the orbit space of any symplectic 4-manifold with a free circle action. A corollary of the main theorem is a formula for the 3-dimensional Seiberg–Witten invariants of the total space of a circle bundle over a surface.

scholarly journals Universality of small black hole instability in AdS/CFT

2017 ◽  
Vol 26 (13) ◽  
pp. 1750140 ◽  
Author(s):  
Alex Buchel
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Einstein Manifolds ◽  
Small Black Hole ◽  
Text Type ◽  
Conformal Field ◽  
Holographic Duals ◽  
Thermal States

[Formula: see text] Type IIb supergravity compactifications on five-dimensional Einstein manifolds [Formula: see text] realize holographic duals to four-dimensional conformal field theories. Black holes in such geometries are dual to thermal states in these CFTs. When black holes become sufficiently small in (global) [Formula: see text], they are expected to suffer Gregory–Laflamme instability with respect to localization on [Formula: see text]. Previously, the instability was demonstrated for gravitational dual of [Formula: see text] SYM, where [Formula: see text]. We extend stability analysis to arbitrary [Formula: see text]. We point out that the quasinormal mode equation governing the instabilities is universal. The precise onset of the instability is [Formula: see text]-sensitive, as it is governed by the lowest nonvanishing eigenvalue [Formula: see text] of its Laplacian.

Rigidity in dimension four of area-minimising Einstein manifolds

2015 ◽  
Vol 158 (2) ◽  
pp. 355-363 ◽  
Author(s):  
A. BARROS ◽  
C. CRUZ ◽  
R. BATISTA ◽  
P. SOUSA
Keyword(s):  
Scalar Curvature ◽  
Ricci Curvature ◽  
Einstein Manifold ◽  
Sharp Inequality ◽  
Positive Scalar Curvature ◽  
Suitable Choice ◽  
Dimensional Manifold ◽  
Einstein Manifolds ◽  
Standard Sphere ◽  
Nonnegative Ricci Curvature

AbstractThe aim of this paper is to prove a sharp inequality for the area of a four dimensional compact Einstein manifold (Σ,gΣ) embedded into a complete five dimensional manifold (M5,g) with positive scalar curvatureRand nonnegative Ricci curvature. Under a suitable choice, we have$area(\Sigma)^{\frac{1}{2}}\inf_{M}R \leq 8\sqrt{6}\pi$. Moreover, occurring equality we deduce that (Σ,gΣ) is isometric to a standard sphere ($\mathbb{S}$4,gcan) and in a neighbourhood of Σ, (M5,g) splits as ((-ϵ, ϵ) ×$\mathbb{S}$4,dt2+gcan) and the Riemannian covering of (M5,g) is isometric to$\Bbb{R}$×$\mathbb{S}$4.

scholarly journals Uplifting dyonic AdS4 black holes on seven-dimensional Sasaki-Einstein manifolds

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Hyojoong Kim ◽  
Nakwoo Kim
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Equations Of Motion ◽  
Page Charge ◽  
Einstein Manifolds ◽  
Charge Quantization ◽  
Black Hole Solutions

Abstract We revisit non-rotating, dyonically charged, and supersymmetric AdS4 black holes, which are solutions of $$ \mathcal{N} $$ N = 2 gauged supergravity with vector- and hyper-multiplets. Uplifting the near horizon solutions to D = 11 supergravity on seven-dimensional Sasaki-Einstein manifolds, we show that dyonic AdS4 black holes correspond to AdS2 solutions with electric and magnetic baryonic fluxes in D = 11 supergravity. We identify the off-shell AdS4 black hole solutions with parameters of D = 11 AdS2 solutions without imposing the equations of motion. We calculate the entropy of dyonic black holes, carefully analyzing the Page charge quantization conditions.

scholarly journals Morphological evolution of supermassive black hole merger hosts and multimessenger signatures

2021 ◽  
Vol 503 (3) ◽  
pp. 3629-3642
Author(s):  
Colin DeGraf ◽  
Debora Sijacki ◽  
Tiziana Di Matteo ◽  
Kelly Holley-Bockelmann ◽  
Greg Snyder ◽  
...  
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Star Formation ◽  
Morphological Evolution ◽  
Full Range ◽  
High Mass ◽  
Morphological Evidence ◽  
Galaxy Mergers ◽  
Host Galaxies ◽  
Supermassive Black Hole

ABSTRACT With projects such as Laser Interferometer Space Antenna (LISA) and Pulsar Timing Arrays (PTAs) expected to detect gravitational waves from supermassive black hole mergers in the near future, it is key that we understand what we expect those detections to be, and maximize what we can learn from them. To address this, we study the mergers of supermassive black holes in the Illustris simulation, the overall rate of mergers, and the correlation between merging black holes and their host galaxies. We find these mergers occur in typical galaxies along the MBH−M* relation, and that between LISA and PTAs we expect to probe the full range of galaxy masses. As galaxy mergers can trigger star formation, we find that galaxies hosting low-mass black hole mergers tend to show a slight increase in star formation rates compared to a mass-matched sample. However, high-mass merger hosts have typical star formation rates, due to a combination of low gas fractions and powerful active galactic nucleus feedback. Although minor black hole mergers do not correlate with disturbed morphologies, major mergers (especially at high-masses) tend to show morphological evidence of recent galaxy mergers which survive for ∼500 Myr. This is on the same scale as the infall/hardening time of merging black holes, suggesting that electromagnetic follow-ups to gravitational wave signals may not be able to observe this correlation. We further find that incorporating a realistic time-scale delay for the black hole mergers could shift the merger distribution towards higher masses, decreasing the rate of LISA detections while increasing the rate of PTA detections.

scholarly journals Islands and stretched horizon

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Yoshinori Matsuo
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Hawking Radiation ◽  
Entanglement Entropy ◽  
Total System ◽  
Island Rule ◽  
Asymptotically Flat ◽  
Flat Spacetime ◽  
Ads Spacetime ◽  
Hole Geometry

Abstract Recently it was proposed that the entanglement entropy of the Hawking radiation contains the information of a region including the interior of the event horizon, which is called “island.” In studies of the entanglement entropy of the Hawking radiation, the total system in the black hole geometry is separated into the Hawking radiation and black hole. In this paper, we study the entanglement entropy of the black hole in the asymptotically flat Schwarzschild spacetime. Consistency with the island rule for the Hawking radiation implies that the information of the black hole is located in a different region than the island. We found an instability of the island in the calculation of the entanglement entropy of the region outside a surface near the horizon. This implies that the region contains all the information of the total system and the information of the black hole is localized on the surface. Thus the surface would be interpreted as the stretched horizon. This structure also resembles black holes in the AdS spacetime with an auxiliary flat spacetime, where the information of the black hole is localized at the interface between the AdS spacetime and the flat spacetime.

scholarly journals Epicyclic Oscillations around Simpson–Visser Regular Black Holes and Wormholes

Universe ◽  
2021 ◽  
Vol 7 (8) ◽  
pp. 279
Author(s):  
Zdeněk Stuchlík ◽  
Jaroslav Vrba
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Active Galactic Nuclei ◽  
Observational Data ◽  
High Frequency ◽  
Galactic Nuclei ◽  
Supermassive Black Holes ◽  
Periodic Oscillations ◽  
High Length ◽  
Circular Geodesic

We study epicyclic oscillatory motion along circular geodesics of the Simpson–Visser meta-geometry describing in a unique way regular black-bounce black holes and reflection-symmetric wormholes by using a length parameter l. We give the frequencies of the orbital and epicyclic motion in a Keplerian disc with inner edge at the innermost circular geodesic located above the black hole outer horizon or on the our side of the wormhole. We use these frequencies in the epicyclic resonance version of the so-called geodesic models of high-frequency quasi-periodic oscillations (HF QPOs) observed in microquasars and around supermassive black holes in active galactic nuclei to test the ability of this meta-geometry to improve the fitting of HF QPOs observational data from the surrounding of supermassive black holes. We demonstrate that this is really possible for wormholes with sufficiently high length parameter l.

scholarly journals Quaternionic contact 4n + 3-manifolds and their 4n-quotients

2021 ◽  
Author(s):  
Yoshinobu Kamishima
Keyword(s):  
Scalar Curvature ◽  
Lie Group ◽  
Contact Structure ◽  
Einstein Manifolds ◽  
Hermitian Metrics ◽  
Kähler Metric ◽  
Formula One ◽  
Quaternion Space ◽  
Kahler Metric ◽  
Do So

AbstractWe study some types of qc-Einstein manifolds with zero qc-scalar curvature introduced by S. Ivanov and D. Vassilev. Secondly, we shall construct a family of quaternionic Hermitian metrics $$(g_a,\{J_\alpha \}_{\alpha =1}^3)$$ ( g a , { J α } α = 1 3 ) on the domain Y of the standard quaternion space $${\mathbb {H}}^n$$ H n one of which, say $$(g_a,J_1)$$ ( g a , J 1 ) is a Bochner flat Kähler metric. To do so, we deform conformally the standard quaternionic contact structure on the domain X of the quaternionic Heisenberg Lie group$${{\mathcal {M}}}$$ M to obtain quaternionic Hermitian metrics on the quotient Y of X by $${\mathbb {R}}^3$$ R 3 .

scholarly journals New non-extremal and BPS hairy black holes in gauged $$ \mathcal{N} $$ = 2 and $$ \mathcal{N} $$ = 8 supergravity

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Andres Anabalon ◽  
Dumitru Astefanesei ◽  
Antonio Gallerati ◽  
Mario Trigiante
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Boundary Conditions ◽  
Charged Black Hole ◽  
Dual Theory ◽  
Real Numbers ◽  
Hairy Black Holes ◽  
Interpolation Parameter ◽  
Black Hole Solutions ◽  
Extremal Black Holes

Abstract In this article we study a family of four-dimensional, $$ \mathcal{N} $$ N = 2 supergravity theories that interpolates between all the single dilaton truncations of the SO(8) gauged $$ \mathcal{N} $$ N = 8 supergravity. In this infinitely many theories characterized by two real numbers — the interpolation parameter and the dyonic “angle” of the gauging — we construct non-extremal electrically or magnetically charged black hole solutions and their supersymmetric limits. All the supersymmetric black holes have non-singular horizons with spherical, hyperbolic or planar topology. Some of these supersymmetric and non-extremal black holes are new examples in the $$ \mathcal{N} $$ N = 8 theory that do not belong to the STU model. We compute the asymptotic charges, thermodynamics and boundary conditions of these black holes and show that all of them, except one, introduce a triple trace deformation in the dual theory.

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