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Motivated by cosmic censorship in general relativity and string theory, we extend Christodoulou's celebrated examples of naked singularity formation in the Einstein-massless scalar field system to include a positive or negative scalar…
We study black hole solutions in general relativity coupled to a unit timelike vector field dubbed the "aether". To be causally isolated a black hole interior must trap matter fields as well as all aether and metric modes. The theory…
Whether the 3D incompressible Euler equations can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics. This work attempts to provide an affirmative answer to…
We construct and investigate the dynamical black hole spacetime embedded in the expanding universe filled with cosmic fluid, such as dark energy. When the equation of state (EoS) parameter of the fluid is a constant, we find exact solutions…
Relativistic and non-relativistic fluid equations can exhibit finite time singular solutions including density singularities appearing in collapse or compression systems and gradient singularities in shock waves. However, only the…
We derive a new formulation of the relativistic Euler equations that exhibits remarkable properties. This new formulation consists of a coupled system of geometric wave, transport, and elliptic equations, sourced by nonlinearities that are…
Classical singularities inside black holes in the Einstein-Yang-Mills theory exhibit unusual features. Only for discrete values of the black hole mass one encounters singularities of the Schwarzschild type (timelike) and the…
This study explores singularity-free solutions to the static, spherical symmetric Einstein equations with the standard Schwarzschild solution as a boundary condition. Imposing the absence of curvature singularities and requiring…
The process of interaction between nonlinear waves on a free surface of a nonconducting fluid in a strong tangential electric field is simulated numerically (effects of the force of gravity and capillarity are neglected). It is shown that…
The thermal view of scalar-tensor gravity is an analogy with a dissipative fluid. The scalar degree of freedom excites gravity to a positive ``temperature'', while Einstein gravity is the ``zero-temperature'' equilibrium state. We extend…
We investigate the problem of metric fluctuations in the presence of the vacuum fluctuations of matter fields and critically assess the usual assertion that vacuum energy implies a Planckian cosmological constant. A new stochastic classical…
We analyze the static and spherically symmetric perfect fluid solutions of Einstein field equations inspired by the non commutative geometry. In the framework of the non commutative geometry this solution is interpreted as a mini black hole…
In this paper we rule out the possibility of asymptotically self-similar singularities for both of the 3D Euler and the 3D Navier-Stokes equations. The notion means that the local in time classical solutions of the equations develop…
We show that a class of finite quantum non-local gravitational theories is conformally invariant at classical as well as at quantum level. This is actually a range of conformal anomaly-free theories in the spontaneously broken phase of the…
We obtain a new class of rotating black holes for Einstein theory with perfect fluid source in (2+1) dimensions. We conclude that these black hole solutions only depend on variable angular velocity $m(r)$. Some examples of these black holes…
The spectrum of known black-hole solutions to the stationary Einstein equations has been steadily increasing, sometimes in unexpected ways. In particular, it has turned out that not all black-hole-equilibrium configurations are…
We prove that singularities propagate globally for viscosity solutions of Hamilton-Jacobi equations related to magnetic mechanical systems on closed Riemannian manifolds. Our main result shows that for any weak KAM solution $u$, the…
We study spherically symmetric geometries made of anisotropic perfect fluid based on general relativity. The purpose of the work is to find and classify black hole solutions in closed spacetime. In a general setting, we find that a static…
A homothetic, static, spherically symmetric solution to the massless Einstein- Klein-Gordon equations is described. There is a curvature singularity which is central, null, bifurcate and marginally trapped. The space-time is therefore…
It has long been suspected that flows of incompressible fluids at large or infinite Reynolds number (namely at small or zero viscosity) may present finite time singularities. We review briefly the theoretical situation on this point. We…