We start with a recently introduced spherically symmetric geodesic fluid model (arXiv: 1601.07030) whose energy-momentum tensor (EMT) in the comoving frame is dust-like with nontrivial energy flux. In the non-comoving...We start with a recently introduced spherically symmetric geodesic fluid model (arXiv: 1601.07030) whose energy-momentum tensor (EMT) in the comoving frame is dust-like with nontrivial energy flux. In the non-comoving energy frame (vanishing energy flux), the same EMT contains besides dust only radial pressure. We present Einstein’s equations together with the matter equations in static spherically symmetric coordinates. These equations are self-contained (four equations for four unknowns). We solve them analytically except for a resulting nonlinear ordinary differential equation (ODE) for the gravitational potential. This ODE can be rewritten as a Lienard differential equation which, however, may be transformed into a rational Abel differential equation of the first kind. Finally, we list some open mathematical problems and outline possible physical applications (galactic halos, dark energy stars) and related open problems.展开更多
We extend the static interior Schwarzschild solution to a collapsing model by applying geometrical methods. We examine the field quantities and field equations in the comoving and non-comoving observer systems. The co...We extend the static interior Schwarzschild solution to a collapsing model by applying geometrical methods. We examine the field quantities and field equations in the comoving and non-comoving observer systems. The collapsing stellar object contracts asymptotically to its minimum extent and needs an infinitely long time to arrive at the final state. The event horizon of the exterior Schwarzschild solution is not reached or even crossed. A geometric model of ECOs (eternally collapsing objects) is presented.展开更多
文摘We start with a recently introduced spherically symmetric geodesic fluid model (arXiv: 1601.07030) whose energy-momentum tensor (EMT) in the comoving frame is dust-like with nontrivial energy flux. In the non-comoving energy frame (vanishing energy flux), the same EMT contains besides dust only radial pressure. We present Einstein’s equations together with the matter equations in static spherically symmetric coordinates. These equations are self-contained (four equations for four unknowns). We solve them analytically except for a resulting nonlinear ordinary differential equation (ODE) for the gravitational potential. This ODE can be rewritten as a Lienard differential equation which, however, may be transformed into a rational Abel differential equation of the first kind. Finally, we list some open mathematical problems and outline possible physical applications (galactic halos, dark energy stars) and related open problems.
文摘We extend the static interior Schwarzschild solution to a collapsing model by applying geometrical methods. We examine the field quantities and field equations in the comoving and non-comoving observer systems. The collapsing stellar object contracts asymptotically to its minimum extent and needs an infinitely long time to arrive at the final state. The event horizon of the exterior Schwarzschild solution is not reached or even crossed. A geometric model of ECOs (eternally collapsing objects) is presented.
