Historical research guide · 0944 · 2019
Collapsing stellar filament and exotic matter in Palatini f(R) gravity
Rubab Manzoor · Abdul Jawad · Muhammad Adeel · Muhammad Saeed · Shamaila Rani
In one minute
Galaxies are not scattered at random. They are strung along filaments, long bridges of visible and dark material that make up the cosmic web. Rubab Manzoor, Abdul Jawad, Muhammad Adeel, Muhammad Saeed and Shamaila Rani ask what happens when one of those filaments collapses under its own gravity, and they ask it inside a theory where the dark part of the universe is not a substance you add but a property of geometry itself. The theory is Palatini f(R) gravity: replace Einstein’s plain curvature term with a general function of curvature, treat the metric and the connection as independent variables, and extra curvature terms appear in the field equations behaving exactly like exotic matter. The authors match the collapsing cylinder to the empty spacetime outside it, derive a collapse equation at the boundary, and find that the filament’s stability is fixed by a balance between the ordinary radial pressure of seen matter and the gravitational pull of those exotic terms. They close with a prediction: dark terms should leave a mark on gravitational waves that pass through them.
Connection
Chapter 3 treats gravity as an induced effect of a background field rather than an irreducible force, and chapter 13 asks what one geometric account of matter and the dark sector would look like. This paper is a worked example of exactly that move: the exotic matter is never added to the universe, it falls out of the geometry — and the authors then ask what it would do to a passing gravitational wave.
From the source
In the Palatini formulation, varying the action with respect to the metric and to the connection separately yields a field equation that can be rewritten in Einstein form, in which the higher-order curvature terms collect into an additional stress-energy tensor alongside the ordinary matter tensor. The dark sector is therefore carried by geometry, not by an added substance.Section 2.1, Equations 6 to 8
The Palatini approach gives second-order, singularity-free equations for the exotic quantities, where the metric approach to f(R) gravity gives fourth-order differential equations that are not easy to handle. The initial-value Cauchy problem in the Palatini approach is both well formulated and well posed, and the theory reproduces the effective dynamics of loop quantum cosmology.Section 1, Introduction, paragraph on the two approaches
Applying the Darmois junction conditions at the collapsing boundary surface — continuity of the first fundamental form and of the extrinsic curvature between the interior filament and the exterior Einstein-Rosen vacuum — yields a collapse equation in which the radial pressure of the baryonic matter does not vanish at the surface. The authors attribute the residual pressure to the momentum flux of the gravitational wave emitted from the cylinder.Section 3, Equation 46
Stability has a simple statement. When collapse stops the boundary velocity vanishes and dissipation of the seen matter becomes negligible, and the collapse equation reduces to a direct balance: the ordinary radial pressure equals the exotic dissipation term less the exotic radial pressure. For a stable configuration the radial pressure of the seen matter is directly proportional to the gravitational effects of the dark terms.Section 4.2, Equations 51 and 52
For a polytropic family of filaments, with radial pressure proportional to a power of the density set by the polytropic index, the stable configurations obey a relation in which the density of the seen material is exponentially related to the gravitational effects of the exotic terms — and the same relation, read the other way, gives the instability criterion for each polytropic index.Section 4.2, Equations 55 to 57
What to watch: taking the sharp-pulse waveform of the radiation emitted outward from the axis, and setting the baryonic stress and dissipation at the boundary to zero, the collapse equation becomes a direct relation between the dark terms and the gravitational wave. The authors conclude that the presence of exotic material can disturb the propagation of gravitational waves — a real observable, which the literature they cite places far below present detector sensitivity.Section 4.3, Equations 58 and 59; Conclusion
The way in
https://doi.org/10.1140/epjc/s10052-019-7332-0How to cite it
Rubab Manzoor, Abdul Jawad, Muhammad Adeel, Muhammad Saeed, Shamaila Rani (2019) Collapsing stellar filament and exotic matter in Palatini f(R) gravity doi:10.1140/epjc/s10052-019-7332-0