scholarly journals SECOND ORDER SCALAR INVARIANTS OF THE RIEMANN TENSOR: APPLICATIONS TO BLACK HOLE SPACETIMES

2002 ◽  
Vol 11 (06) ◽  
pp. 827-841 ◽  
Author(s):  
CHRISTIAN CHERUBINI ◽  
DONATO BINI ◽  
SALVATORE CAPOZZIELLO ◽  
REMO RUFFINI
Keyword(s):  
Black Hole ◽  
Riemann Tensor ◽  
Second Order ◽  
Black Hole Spacetimes ◽  
Definition Of ◽  
Scalar Invariants

We discuss the Kretschmann, Chern–Pontryagin and Euler invariants among the second order scalar invariants of the Riemann tensor in any spacetime in the Newman–Penrose formalism and in the framework of gravitoelectromagnetism, using the Kerr–Newman geometry as an example. An analogy with electromagnetic invariants leads to the definition of regions of gravitoelectric or gravitomagnetic dominance.

Dynamical black holes

2020 ◽  
pp. 312-336
Author(s):  
Piotr T. Chruściel
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Cauchy Data ◽  
Einstein Equations ◽  
Black Hole Spacetimes ◽  
Alternative Approaches ◽  
Definition Of ◽  
Meaningful Definition ◽  
Stability Results ◽  
Black Hole Solutions

In this chapter we review what is known about dynamical black hole-solutions of Einstein equations. We discuss the Robinson–Trautman black holes, with or without a cosmological constant. We review the Cauchy-data approach to the construction of black-hole spacetimes. We propose some alternative approaches to a meaningful definition of black hole in a dynamical spacetime, and we review the nonlinear stability results for black-hole solutions of vacuum Einstein equations.

scholarly journals Noncommutative Reissner–Nordstrøm black hole

2018 ◽  
Vol 96 (12) ◽  
pp. 1259-1265 ◽  
Author(s):  
Carlos A. Soto-Campos ◽  
Susana Valdez-Alvarado
Keyword(s):  
Black Hole ◽  
Fourth Order ◽  
Riemannian Geometry ◽  
Deformation Parameter ◽  
Riemann Tensor ◽  
Quantum Level ◽  
Metric Tensor ◽  
Noncommutative Version ◽  
Curvature Tensors ◽  
Scalar Invariants

In this work we construct a deformed embedding of the Reissner–Nordstrøm (R-N) space–time within the framework of a noncommutative Riemannian geometry. We provide noncommutative corrections to the usual Riemannian expressions for the metric and curvature tensors. For the case of the metric tensor, the expression obtained possesses terms that are valid to all orders in the deformation parameter. Then we calculate the correction to the area of the event horizon of the corresponding noncommutative R-N black hole, obtaining an expression for the area of the black hole, which is correct up to fourth-order terms in the deformation parameter. Finally we include some comments on the noncommutative version on one of the second-order scalar invariants of the Riemann tensor, the so-called Kretschmann invariant, a quantity that is regularly used to extend gravity to the quantum level.

scholarly journals Classical black hole scattering from a worldline quantum field theory

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Gustav Mogull ◽  
Jan Plefka ◽  
Jan Steinhoff
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Black Hole ◽  
Quantum Field ◽  
Expectation Values ◽  
Path Integral Representation ◽  
S Matrix ◽  
Feynman Rules ◽  
Definition Of ◽  
Three Body

Abstract A precise link is derived between scalar-graviton S-matrix elements and expectation values of operators in a worldline quantum field theory (WQFT), both used to describe classical scattering of black holes. The link is formally provided by a worldline path integral representation of the graviton-dressed scalar propagator, which may be inserted into a traditional definition of the S-matrix in terms of time-ordered correlators. To calculate expectation values in the WQFT a new set of Feynman rules is introduced which treats the gravitational field hμν(x) and position $$ {x}_i^{\mu}\left({\tau}_i\right) $$ x i μ τ i of each black hole on equal footing. Using these both the 3PM three-body gravitational radiation 〈hμv(k)〉 and 2PM two-body deflection $$ \Delta {p}_i^{\mu } $$ Δ p i μ from classical black hole scattering events are obtained. The latter can also be obtained from the eikonal phase of a 2 → 2 scalar S-matrix, which we show corresponds to the free energy of the WQFT.

scholarly journals Stable circular orbits in caged black hole spacetimes

2021 ◽  
Vol 103 (8) ◽  
Author(s):  
Takahisa Igata ◽  
Shinya Tomizawa
Keyword(s):  
Black Hole ◽  
Circular Orbits ◽  
Black Hole Spacetimes

scholarly journals Master equations and quasinormal modes of spin- 3/2 fields in Schwarzschild (A)dS black hole spacetimes

2019 ◽  
Vol 100 (10) ◽  
Author(s):  
Chun-Hung Chen ◽  
Hing-Tong Cho ◽  
Alan S. Cornell ◽  
Gerhard E. Harmsen
Keyword(s):  
Black Hole ◽  
Quasinormal Modes ◽  
Master Equations ◽  
Black Hole Spacetimes
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