Results 41 to 50 of about 685,590 (201)
Black Holes have Intrinsic Scalar Curvature
Reports in Advances of Physical Sciences, 2023 The scalar curvature R is invariant under isometric symmetries (distance invariance) associated with metric spaces. Gravitational Riemannian manifolds are metric spaces.
P. D. Morley
doaj +1 more source
AIMS MathematicsThe Ricci curvature in Finsler geometry naturally generalizes the Ricci curvature in Riemannian geometry. In this paper, we study the -th root metric with weakly isotropic scalar curvature and obtain that its scalar curvature must vanish.
Xiaoling Zhang, Cuiling Ma, Lili Zhao
doaj +1 more source
European Physical Journal C: Particles and Fields, 2023 The observational data of primordial black holes and scalar-induced gravitational waves can constrain the primordial curvature perturbation at small scales. We parameterize the primordial curvature perturbation by a broken power law form and find that it
Zhu Yi, Qin Fei
doaj +1 more source
Mean Curvature in the Light of Scalar Curvature [PDF]
, 2018 We formulate several conjectures on mean convex domains in the Euclidean spaces, as well as in more general spaces with lower bonds on their scalar curvatures, and prove a few theorems motivating these conjectures.
M. Gromov
semanticscholar +1 more source
Infinite loop spaces and positive scalar curvature in the presence of a fundamental group [PDF]
Geometry and Topology, 2017 This is a continuation of our previous work with Botvinnik on the nontriviality of the secondary index invariant on spaces of metrics of positive scalar curvature, in which we take the fundamental group of the manifolds into account.
Johannes Ebert, O. Randal-Williams
semanticscholar +1 more source
On Hawking mass and Bartnik mass of CMC surfaces
, 2019 Given a constant mean curvature surface that bounds a compact manifold with nonnegative scalar curvature, we obtain intrinsic conditions on the surface that guarantee the positivity of its Hawking mass.
Miao, Pengzi, Wang, Yaohua, Xie, Naqing
core +1 more source
Intrinsic problems of the gravitational baryogenesis
Physics Letters B, 2017 Modification of gravity due to the curvature dependent term in the gravitational baryogenesis scenario is considered. It is shown that this term leads to the fourth order differential equation of motion for the curvature scalar instead of the algebraic ...
E.V. Arbuzova, A.D. Dolgov
doaj +1 more source
Scalar curvature and singular metrics [PDF]
, 2016 Let $M^n$, $n\ge3$, be a compact differentiable manifold with nonpositive Yamabe invariant $\sigma(M)$. Suppose $g_0$ is a continuous metric with $V(M, g_0)=1$, smooth outside a compact set $\Sigma$, and is in $W^{1,p}_{loc}$ for some $p>n$.
Yuguang Shi, Luen-Fai Tam
semanticscholar +1 more source
Thermodynamic Geometry and Phase Transitions in Kerr-Newman-AdS Black Holes
, 2010 We investigate phase transitions and critical phenomena in Kerr-Newman-Anti de Sitter black holes in the framework of the geometry of their equilibrium thermodynamic state space. The scalar curvature of these state space Riemannian geometries is computed
A Chamblin +44 more
core +1 more source
Scalar Curvature via Local Extent
Analysis and Geometry in Metric Spaces, 2018 We give a metric characterization of the scalar curvature of a smooth Riemannian manifold, analyzing the maximal distance between (n + 1) points in infinitesimally small neighborhoods of a point.
Veronelli Giona
doaj +1 more source