Dear Einstein Toolkit Users and Maintainers,

My name is Shaun Osgathorpe. I am an independent amateur researcher based in the UK, without a university affiliation or PhD, and I am contacting the Einstein Toolkit community because I would like to determine whether a physical hypothesis I have been developing can be tested properly using established numerical-relativity and GRMHD methods.

I want to be clear from the beginning that I am not presenting the hypothesis as established physics. My objective is to test it rigorously and allow the numerical results to reject, modify or support individual parts of the model.

I have been developing a proposed multi-stage scenario involving pre-existing matter, gravitational interactions, collisions, shocks, cooling, magnetic fields and eventual gravitational gathering and possible star formation.

The current proposed sequence is broadly:

Pre-existing matter and gas → gravitational/tidal interaction → collision or close interaction → compression, shocks, heating and mixing → cooling and radiation → sustained gathering/convergence where physically permitted → possible gravitationally bound structure → possible gravitational contraction → fragmentation or protostellar formation if the equations permit it → eventual stellar and planetary-system evolution.

An important part of the model is that I do NOT assume that a collision creates a star. A collision would only change the physical environment. Gathering and gravitational collapse would also be treated as separate outcomes rather than assuming that one automatically follows the other.

I have also been investigating a possible role for neutron-star merger ejecta. The proposed mechanism is not that a neutron-star merger creates an entire star or gas cloud by itself. Instead, neutron-rich ejecta and heavy-element enrichment would interact with pre-existing gas, while nearby gravitational interactions could alter and compress that material. Subsequent cooling, accretion and gravitational instability would then have to develop naturally.

I would like to test whether this is physically viable rather than assume that it is.

The numerical experiment I eventually want to perform would include, where appropriate:

• 3D hydrodynamics/GRMHD • self-gravity • spatially varying density, pressure, temperature and velocity • collision velocity and impact parameter • angular momentum and rotation • tidal fields and tidal-tensor eigenvalues • magnetic-field strength, geometry and orientation • magnetic pressure and magnetic tension • radiative cooling and energy loss • appropriate equations of state • neutron-rich material/ejecta • pulsar or magnetised compact-object electromagnetic forcing • gravitational-wave tidal effects • adaptive mesh refinement • multiple numerical resolutions • convergence testing.

I would particularly like to investigate whether magnetic fields and time-dependent electromagnetic fields can alter gathering, compression, turbulence, angular-momentum transport or fragmentation.

For gravitational waves, I do not want to model them simply as an attractive or repulsive force. I understand that their local effect is an alternating tidal distortion. For a simple + polarised linearised wave, for example, the relative accelerations can be represented schematically as

a_x = (1/2) h¨ x

a_y = -(1/2) h¨ y.

A production calculation should preferably generate the gravitational radiation self-consistently through numerical relativity rather than impose an arbitrary force.

I have already performed reduced numerical experiments locally to test parts of the mathematics and to identify useful parameter ranges.

These have included:

• 3D self-gravitating particle calculations • corrected gravitational-wave tidal forcing • magnetic/pulsar forcing proxies • cooling • gathering diagnostics • bound-state diagnostics • Jeans diagnostics • resolution refinement • timestep refinement • parameter sweeps • conservation checks.

The reduced calculations have produced interesting behaviour, but I do not regard them as astrophysical evidence. In particular, I have found that the apparent effect of gravitational waves can be very small and can change with parameters. This is exactly why I would like to move toward a proper production calculation rather than extrapolate from a simplified model.

One reduced Stage 3–8 parameter sweep, for example, produced the following fractions of its deliberately sampled parameter space:

Gathering diagnostic: 90.102% Bound diagnostic: 33.371% Jeans diagnostic: 14.625% Cooling-time/free-fall diagnostic: 87.606% All combined reduced criteria: 5.589%

These numbers are NOT being presented as probabilities of star formation. They are simply outputs from a chosen synthetic parameter space.

I would therefore like expert guidance on whether the proposed numerical experiment can be formulated correctly using the Einstein Toolkit.

In particular, I would appreciate advice on:

1. Whether Einstein Toolkit is an appropriate framework for this problem. 2. Which existing Einstein Toolkit components would be most appropriate. 3. Whether GRHayL/IllinoisGRMHD and CarpetX/AMR would be suitable starting points. 4. How best to represent the gas, magnetic fields, compact-object interaction and radiation. 5. Whether the proposed gravitational-wave treatment is appropriate. 6. What aspects of the model should be removed because they are physically unjustified. 7. What initial conditions would be scientifically defensible. 8. What resolution would be required before conclusions could be trusted. 9. Whether a smaller test case could be run first before attempting a large HPC calculation. 10. Whether there is an appropriate tutorial, community project or researcher who could advise an independent new user.

I would also like to use matched controls, for example:

A. Gravity + tides B. Gravity + magnetic fields C. Gravity + cooling D. Gravity + magnetic fields + cooling E. Gravity + gravitational waves F. Gravity + gravitational waves + magnetic fields G. Gravity + gravitational waves + magnetic fields + pulsar electromagnetic forcing

with corresponding no-GW, no-magnetic-field, no-cooling and no-rotation controls.

The key scientific question is not "can I make the simulation form a star?"

It is:

"Under what initial conditions, if any, do the established equations produce sustained gathering, a gravitationally bound structure, contraction, fragmentation and eventual protostellar formation, and which physical mechanisms materially affect that outcome?"

I would be very grateful for any advice from members of the Einstein Toolkit community, including advice that shows the hypothesis is incorrectly formulated.

I am also willing to start with a much smaller and simpler problem if that is the scientifically appropriate route.

I understand that I am an amateur and that a production numerical-relativity calculation requires considerably more expertise than I currently have. I am therefore approaching the community primarily for technical and scientific guidance rather than assuming that my proposed model is correct.

If useful, I can provide the equations, parameter ranges, reduced numerical results, control matrix and numerical job specification that I have developed so far.

Thank you for taking the time to read this, and for any guidance you may be able to provide.

Kind regards,

Shaun Osgathorpe Independent researcher United Kingdom