The Experts below are selected from a list of 273 Experts worldwide ranked by ideXlab platform
Takahiro Tanaka - One of the best experts on this subject based on the ideXlab platform.
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a simple diagnosis of non smoothness of black hole horizon curvature singularity at horizons in extremal kaluza klein black holes
Classical and Quantum Gravity, 2015Co-Authors: Masashi Kimura, Hideki Ishihara, Ken Matsuno, Takahiro TanakaAbstract:We propose a simple method to prove non-smoothness of a black hole horizon. The existence of a C1 extension across the horizon implies that there is no extension across the horizon if some components of the Nth covariant derivative of the Riemann Tensor diverge at the horizon in the coordinates of the C1 extension. In particular, the divergence of a component of the Riemann Tensor at the horizon directly indicates the presence of a curvature singularity. By using this method, we can confirm the existence of a curvature singularity for several cases where the scalar invariants constructed from the Riemann Tensor, e.g., the Ricci scalar and the Kretschmann invariant, take finite values at the horizon. As a concrete example of the application, we show that the Kaluza–Klein black holes constructed by Myers have a curvature singularity at the horizon if the spacetime dimension is higher than five.
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A simple diagnosis of non-smoothness of black hole horizon: curvature singularity at horizons in extremal Kaluza–Klein black holes
Classical and Quantum Gravity, 2014Co-Authors: Masashi Kimura, Hideki Ishihara, Ken Matsuno, Takahiro TanakaAbstract:We propose a simple method to prove non-smoothness of a black hole horizon. The existence of a C1 extension across the horizon implies that there is no extension across the horizon if some components of the Nth covariant derivative of the Riemann Tensor diverge at the horizon in the coordinates of the C1 extension. In particular, the divergence of a component of the Riemann Tensor at the horizon directly indicates the presence of a curvature singularity. By using this method, we can confirm the existence of a curvature singularity for several cases where the scalar invariants constructed from the Riemann Tensor, e.g., the Ricci scalar and the Kretschmann invariant, take finite values at the horizon. As a concrete example of the application, we show that the Kaluza–Klein black holes constructed by Myers have a curvature singularity at the horizon if the spacetime dimension is higher than five.
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a simple diagnosis of non smoothness of black hole horizon curvature singularity at horizons in extremal kaluza klein black holes
arXiv: General Relativity and Quantum Cosmology, 2014Co-Authors: Masashi Kimura, Hideki Ishihara, Ken Matsuno, Takahiro TanakaAbstract:We propose a simple method to prove non-smoothness of a black hole horizon. The existence of a $C^1$ extension across the horizon implies that there is no $C^{N + 2}$ extension across the horizon if some components of $N$-th covariant derivative of Riemann Tensor diverge at the horizon in the coordinates of the $C^1$ extension. In particular, the divergence of a component of the Riemann Tensor at the horizon directly indicates the presence of a curvature singularity. By using this method, we can confirm the existence of a curvature singularity for several cases where the scalar invariants constructed from the Riemann Tensor, e.g., the Ricci scalar and the Kretschmann invariant, take finite values at the horizon. As a concrete example of the application, we show that the Kaluza-Klein black holes constructed by Myers have a curvature singularity at the horizon if the spacetime dimension is higher than five.
Kayll Lake - One of the best experts on this subject based on the ideXlab platform.
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invariants of the Riemann Tensor for class b warped product space times
Computer Physics Communications, 1998Co-Authors: Kevin Santosuosso, Denis Pollney, Nicos Pelavas, Peter Musgrave, Kayll LakeAbstract:Abstract We use the computer algebra system GRTensorII to examine invariants polynomial in the Riemann Tensor for class B warped product space-times — those which can be decomposed into the coupled product of two 2-dimensional spaces, one Lorentzian and one Riemannian, subject to the separability of the coupling ds2 = dsϵ12 (u,v) + C(xγ)2dsϵ22 (θ, φ). with C(xγ)2 = r(u,v)2w(θ, φ)2 and sig(ϵ1) = 0, sig(ϵ2) = 2ϵ ( ϵ = ± 1) for class B1 space-times and sig(ϵ1) = 2ϵ, sig(ϵ2) = 0 for class B2. Although very special, these spaces include many of interest, for example, all spherical, plane, and hyperbolic space-times. The first two Ricci invariants along with the Ricci scalar and the real component of the second Weyl invariant J alone are shown to constitute the largest independent set of invariants to degree five for this class. Explicit syzygies are given for other invariants up to this degree. It is argued that this set constitutes the largest functionally independent set to any degree for this class, and some physical consequences of the syzygies are explored.
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Invariants of the Riemann Tensor for Class B Warped Product Spacetimes
Computer Physics Communications, 1998Co-Authors: Kevin Santosuosso, Denis Pollney, Nicos Pelavas, Peter Musgrave, Kayll LakeAbstract:We use the computer algebra system \textit{GRTensorII} to examine invariants polynomial in the Riemann Tensor for class $B$ warped product spacetimes - those which can be decomposed into the coupled product of two 2-dimensional spaces, one Lorentzian and one Riemannian, subject to the separability of the coupling: $ds^2 = ds_{\Sigma_1}^2 (u,v) + C(x^\gamma)^2 ds_{\Sigma_2}^2 (\theta,\phi)$ with $C(x^\gamma)^2=r(u,v)^2 w(\theta,\phi)^2$ and $sig(\Sigma_1)=0, sig(\Sigma_2)=2\epsilon (\epsilon=\pm 1)$ for class $B_{1}$ spacetimes and $sig(\Sigma_1)=2\epsilon, sig(\Sigma_2)=0$ for class $B_{2}$. Although very special, these spaces include many of interest, for example, all spherical, plane, and hyperbolic spacetimes. The first two Ricci invariants along with the Ricci scalar and the real component of the second Weyl invariant $J$ alone are shown to constitute the largest independent set of invariants to degree five for this class. Explicit syzygies are given for other invariants up to this degree. It is argued that this set constitutes the largest functionally independent set to any degree for this class, and some physical consequences of the syzygies are explored.
Silvio Pallua - One of the best experts on this subject based on the ideXlab platform.
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Conformal entropy and stationary Killing horizons
Journal of Physics: Conference Series, 2006Co-Authors: Maro Cvitan, Silvio Pallua, Predrag Dominis PresterAbstract:Using Virasoro algebra approach, black hole entropy formula for a general class of higher curvature Lagrangians with arbitrary dependence on Riemann Tensor can be obtained from properties of stationary Killing horizons. The properties used are a consequence of regularity of invariants of Riemann Tensor on the horizon. As suggested by an example Lagrangian, eventual generalisation of these results to Lagrangians with derivatives of Riemann Tensor, would require assuming regularity of invariants involving derivatives of Riemann Tensor and that would lead to additional restrictions on metric functions near horizon.
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Stationary Killing horizons and conformal entropy in higher order gravity theories
AIP Conference Proceedings, 2006Co-Authors: Maro Cvitan, Silvio Pallua, Predrag Dominis PresterAbstract:Boundary conditions, that follow from regularity of invariants of Riemann Tensor on the horizon, can be used to derive microscopic entropy formula, based on Virasoro approach, for Lagrangians with arbitrary dependence on Riemann Tensor. An example of a Lagrangian with derivatives of Riemann Tensor suggests that boundary conditions can be obtained from regularity of invariants involving derivatives of Riemann Tensor and that leads to new properties of metric functions near horizon.
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Conformal entropy for generalized gravity theories as a consequence of horizon properties
Physical Review D, 2005Co-Authors: Maro Cvitan, Silvio PalluaAbstract:We show that a microscopic entropy formula based on Virasoro algebra follows from properties of stationary Killing horizons for Lagrangians with arbitrary dependence on Riemann Tensor. The properties used are a consequence of regularity of invariants of Riemann Tensor on the horizon. Eventual generalization of these results to Lagrangians with derivatives of Riemann Tensor, as suggested by an example treated in the paper, relies on assuming regularity of invariants involving derivatives of Riemann Tensor. This assumption however leads also to new interesting restrictions on metric functions near the horizon.
Masashi Kimura - One of the best experts on this subject based on the ideXlab platform.
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a simple diagnosis of non smoothness of black hole horizon curvature singularity at horizons in extremal kaluza klein black holes
Classical and Quantum Gravity, 2015Co-Authors: Masashi Kimura, Hideki Ishihara, Ken Matsuno, Takahiro TanakaAbstract:We propose a simple method to prove non-smoothness of a black hole horizon. The existence of a C1 extension across the horizon implies that there is no extension across the horizon if some components of the Nth covariant derivative of the Riemann Tensor diverge at the horizon in the coordinates of the C1 extension. In particular, the divergence of a component of the Riemann Tensor at the horizon directly indicates the presence of a curvature singularity. By using this method, we can confirm the existence of a curvature singularity for several cases where the scalar invariants constructed from the Riemann Tensor, e.g., the Ricci scalar and the Kretschmann invariant, take finite values at the horizon. As a concrete example of the application, we show that the Kaluza–Klein black holes constructed by Myers have a curvature singularity at the horizon if the spacetime dimension is higher than five.
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A simple diagnosis of non-smoothness of black hole horizon: curvature singularity at horizons in extremal Kaluza–Klein black holes
Classical and Quantum Gravity, 2014Co-Authors: Masashi Kimura, Hideki Ishihara, Ken Matsuno, Takahiro TanakaAbstract:We propose a simple method to prove non-smoothness of a black hole horizon. The existence of a C1 extension across the horizon implies that there is no extension across the horizon if some components of the Nth covariant derivative of the Riemann Tensor diverge at the horizon in the coordinates of the C1 extension. In particular, the divergence of a component of the Riemann Tensor at the horizon directly indicates the presence of a curvature singularity. By using this method, we can confirm the existence of a curvature singularity for several cases where the scalar invariants constructed from the Riemann Tensor, e.g., the Ricci scalar and the Kretschmann invariant, take finite values at the horizon. As a concrete example of the application, we show that the Kaluza–Klein black holes constructed by Myers have a curvature singularity at the horizon if the spacetime dimension is higher than five.
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a simple diagnosis of non smoothness of black hole horizon curvature singularity at horizons in extremal kaluza klein black holes
arXiv: General Relativity and Quantum Cosmology, 2014Co-Authors: Masashi Kimura, Hideki Ishihara, Ken Matsuno, Takahiro TanakaAbstract:We propose a simple method to prove non-smoothness of a black hole horizon. The existence of a $C^1$ extension across the horizon implies that there is no $C^{N + 2}$ extension across the horizon if some components of $N$-th covariant derivative of Riemann Tensor diverge at the horizon in the coordinates of the $C^1$ extension. In particular, the divergence of a component of the Riemann Tensor at the horizon directly indicates the presence of a curvature singularity. By using this method, we can confirm the existence of a curvature singularity for several cases where the scalar invariants constructed from the Riemann Tensor, e.g., the Ricci scalar and the Kretschmann invariant, take finite values at the horizon. As a concrete example of the application, we show that the Kaluza-Klein black holes constructed by Myers have a curvature singularity at the horizon if the spacetime dimension is higher than five.
Don N. Page - One of the best experts on this subject based on the ideXlab platform.
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Nonvanishing Local Scalar Invariants even in VSI Spacetimes with all Polynomial Curvature Scalar Invariants Vanishing
Classical and Quantum Gravity, 2009Co-Authors: Don N. PageAbstract:VSI ('vanishing scalar invariant') spacetimes have zero values for all total scalar contractions of all polynomials in the Riemann Tensor and its covariant derivatives. However, there are other ways of concocting local scalar invariants (nonpolynomial) from the Riemann Tensor that need not vanish even in VSI spacetimes, such as Cartan invariants. Simple examples are given that reduce to the squared amplitude for a linearized monochromatic plane gravitational wave. These nonpolynomial local scalar invariants are also evaluated for non-VSI spacetimes such as Schwarzschild and Kerr and are estimated near the surface of the earth. Similar invariants are defined for null fluids and for electromagnetic fields.
