## 25 Citations

### An Exploration of the Singularities in General Relativity

- Physics
- 2012

In General Relativity, spacetime singularities raise a number of problems, both mathematical and physical. One can identify a class of singularities { with smooth but degenerate metric { which, under…

### Singular General Relativity

- Physics
- 2015

This work presents the foundations of Singular Semi-Riemannian Geometry and Singular General Relativity, based on the author's research. An extension of differential geometry and of Einstein's…

### The Good Properties of Schwarzschild’s Singularity

- Physics
- 2018

The most notable problems of General Relativity (GR), such as the occurrence of singularities and the information paradox, were initially found on the background provided by Schwarzschild’s solution.…

### Gauge theory at singularities

- Mathematics
- 2014

Building on author’s previous results in singular semi-Riemannian geometry and singular general relativity, the behavior of gauge theory at singularities is analyzed. The usual formulations of the…

### THE MEANING OF SPACETIME SINGULARITIES

- Physics
- 2016

In the following, I will discuss the geometric and physical interpretation of spacetime singularities occurring in general relativity (GR). GR has two main problems: the prediction of singularities…

### The problem of singularities in General Relativity 2 3 . The mathematical methods : Singular Semi-Riemannian Geometry 4 4

- Physics
- 2014

Recent results show that important singularities in General Relativity can be naturally described in terms of finite and invariant canonical geometric objects. Consequently, one can write field…

### The Geometry of Black Hole Singularities

- Physics
- 2014

Recent results show that important singularities in General Relativity can be naturally described in terms of finite and invariant canonical geometric objects. Consequently, one can write field…

### Kerr-Newman Solutions with Analytic Singularity and no Closed Timelike Curves

- Mathematics
- 2011

It is shown that the Kerr-Newman solution, representing charged and rotating stationary black holes, admits analytic extension at the singularity. This extension is obtained by using new coordinates,…

### Did God Divide by Zero ?

- Physics
- 2012

It is said that General Relativity fails, because of the occurrence of singularities, and of the non-renormalizability of Quantum Gravity. Is this failure due to General Relativity, or to our limited…

## References

SHOWING 1-10 OF 35 REFERENCES

### Spacetimes with singularities

- Mathematics
- 2012

Abstract We report on some advances made in the problem of singularities in general relativity. First is introduced the singular semi-Riemannian geometry for metrics which can change their signature…

### Schwarzschild’s singularity is semi-regularizable

- Mathematics
- 2012

It is shown that the Schwarzschild spacetime can be extended so that the metric becomes analytic at the singularity. The singularity continues to exist, but it is made degenerate and smooth, and the…

### Cosmological models: Cargese lectures 1998

- Physics
- 1998

The aim of this set of lectures is a systematic presentation of a 1 + 3 covariant approach to studying the geometry, dynamics, and observational properties of relativistic cosmological models. In…

### Isotropic cosmological singularities: other matter models

- Physics, Mathematics
- 2002

Isotropic cosmological singularities are singularities which can be removed by rescaling the metric. In some cases already studied ([2], [1]) existence and uniqueness of cosmological models with data…

### On singular semi-Riemannian manifolds

- Mathematics
- 2014

On a Riemannian or a semi-Riemannian manifold, the metric determines invariants like the Levi-Civita connection and the Riemann curvature. If the metric becomes degenerate (as in singular…

### Riemannian Geometry

- MathematicsNature
- 1927

THE recent physical interpretation of intrinsic differential geometry of spaces has stimulated the study of this subject. Riemann proposed the generalisation, to spaces of any order, of Gauss's…

### Cosmological models (Carg\`{e}se lectures 1998)

- Physics
- 1998

The aim of this set of lectures is a systematic presentation of a 1+3 covariant approach to studying the geometry, dynamics, and observational properties of relativistic cosmological models. In…

### Isotropic Cosmological Singularities: I. Polytropic Perfect Fluid Spacetimes

- Mathematics, Physics
- 1999

Abstract We consider the conformal Einstein equations for 1⩽ γ ⩽2 polytropic perfect fluid cosmologies which admit an isotropic singularity. For 1 γ ⩽2 it is shown that the Cauchy problem for these…

### Beyond the Friedmann—Lemaître—Robertson—Walker Big Bang Singularity

- Mathematics
- 2012

Einstein's equation, in its standard form, breaks down at the Big Bang singularity. A new version, equivalent to Einstein's whenever the latter is defined, but applicable in wider situations, is…

### Exact Solutions of Einstein's Field Equations

- Physics
- 2004

We examine various well known exact solutions available in the literature to investigate the recent criterion obtained in Negi and Durgapal [Gravitation and Cosmology7, 37 (2001)] which should be…